Exam 9: Hypothesis Testing

You want to test if more than 20% of homes in a neighborhood have recently been sold through a short sale, at a foreclosure auction, or by the bank following an unsuccessful foreclosure auction. You take a sample of 60 homes from this neighborhood and find that 14 fit your criteria. The appropriate null and alternative hypotheses are ________.

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350.To determine whether there has been a decrease in the average number of customers visiting the dealership daily, the appropriate hypotheses are ________.

A philanthropic organization helped a town in Africa dig several wells to gain access to clean water. Before the wells were in place, an average of 120 infants contracted typhoid each month. After the wells were installed, the philanthropic organization surveyed for nine months and found an average of 90 infants contracted typhoid per month. Assume that the population standard deviation is 40 and the number of infants that contract typhoid is normally distributed. A) Specify the null and alternative hypotheses to determine whether the average number of infants that contract typhoid has decreased because the wells were put in place. B) Calculate the value of the test statistic and the p-value. C) At the 5% significance level, can you conclude that the number of babies falling ill due to typhoid has decreased? Explain.

Construct the null and alternative hypotheses for the following claims. A) "The school's mean GPA differs from 2.50 GPA." B) "The school's mean GPA is less than 2.50 GPA."

When conducting a hypothesis test concerning the population proportion, the value of the test statistic is calculated as ________.

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16-through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. When testing whether the dropout rate has decreased, the appropriate hypotheses are ________.

A Type I error is committed when we reject the null hypothesis, which is actually true.

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 18 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds. The test statistic for this hypothesis would be ________.

The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later, School Buses Still Late," Boston Globe, October 5). Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route. Historically, the bus service on the route has been, on average, 12 minutes late. After the schedule adjustment, the first 36 runs were an average of eight minutes late. As a result, the Boston public school district claimed that the schedule adjustment was an improvement-students were not as late. Assume a population standard deviation for bus arrival time of 12 minutes. The value of the test statistic is ________.

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 18 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds. Which of the following are appropriate hypotheses to test the advertisement's claim?

A hairdresser believes that she is more profitable on Tuesdays, her lucky day of the week. She knows that, on average, she has a daily revenue of $250. She randomly samples the revenue from eight Tuesdays and finds she takes in $260, $245, $270, $260, $295, $235, $270, and $265. Assume that daily revenue is normally distributed. A) Specify the population parameter to be tested. B) Specify the null and alternative hypotheses to test the hairdresser's claim. C) Calculate the sample mean revenue and the sample standard deviation. D) Compute the value of the appropriate test statistic. E) At the 10% significance level, calculate the p-value. F) At the 10% significance level, is the hairdresser's claim supported by the data?

A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86]. At the 1% significance level, what decision should be made regarding the following hypothesis test with H₀: μ = 0, H_A: μ ≠ 0?

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. At a 5% significance level, the decision is to ________.

If the p-value for a hypothesis test is 0.027 and the chosen level of significance is α = 0.05, then the correct conclusion is to ________.

In general, the null and alternative hypotheses are ________.

A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. If this is to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network receives 827 responses, of which 428 indicate they would like to see the new show in the lineup. Which of the following is an appropriate hypothesis to test if the television network should give its newest show a spot during prime time at night?

A recent report claimed that Americans are retiring later in life (U.S. News & World Report, August 17). An economist wishes to determine if the mean retirement age has increased from 62. To conduct the relevant test, she takes a random sample of 38 Americans who have recently retired and computes the value of the test statistic as t₃₇ = 1.92. With α = 0.05, she ________.

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. The population parameter to be tested is ________.

A professional baseball player changed his throwing motion to increase the velocity of his fastball. Before the change, the player threw his fastball at an average of 91 miles per hour. After the change in his throwing motion, the team watched him throw 64 fastballs with an average speed of 91.75 miles per hour and a standard deviation of 3 miles per hour. A) Specify the null and alternative hypotheses to determine whether the baseball player increased the speed of his fastball. B) Calculate the value of the test statistic and the p-value. C) At the 1% significance level, can you conclude that the baseball player has increased the speed of his fastball? Explain.

On the basis of sample information, we either "accept the null hypothesis" or "reject the null hypothesis."